My understanding from the trailers is that Cumberbatch is on the bridge until the ship comes to a stop and he jumps out of the broken viewscreen/window onto the rubble and makes his escape.

The ship crashes into the harbor, doesn't it?

Harrison watches the London bombing, not the ship crash.

No real spoilers here, since it can all be pieced together from trailers: the Dreadnought crashes into the harbor and momentum carries it well into the city. Harrison dusts himself off, hangs out the broken viewscreen and stares at the damage below. He then somehow gets out of the ship and runs like hell through various windows.

Now for the spoiler part:

Spock vows vengeance after Kirk's death and the obligatory "KHAAAAAAAAANNNNNNN!" scream, and likely beams down to beat the living, genetically-enhanced shit out of him. The fight scene on the barges ensues. I haven't seen the movie, just surmised this from the trailers, but I hope there's a more climactic ending than this.

You have the basic idea right, but...

Both Spock and Uhura pursue Khan because McCoy needs his blood to save Kirk. Don't know if Spock does the Khan scream, but someone other than Kirk does...